[seqfan] Re: What is the base 36 log of 10077696?

[Jim Nastos]

Quick follow-up.
again, on Wolfram Alpha:
log_36(2^k * 3^k) evaluates perfectly to an integer for each even k,
while for odd k it evaluates to a proper fraction just in the k=3 case.
k=5 report:

log_36(2^5 * 3^5) = log(7776) / log(36) = 2.499999999999999...
J


On Mon, Apr 18, 2011 at 4:13 PM, Jim Nastos <nastos at gmail.com> wrote:

> It is interesting behaviour... even in the online Wolfram Alpha:
> The exact value of your logarithm is reported as the quotient of logs, and
> its associated "approximate form" (i.e. floating point evaluation) displays
> as 4.499999999999999999999999999999...
>
> I am guessing that if a desired logarithm result is non-integer, a separate
> numerical subroutine is used.
> J
>
>   On Mon, Apr 18, 2011 at 4:01 PM, Alonso Del Arte <
> alonso.delarte at gmail.com> wrote:
>
>> What is the base 36 log of 10077696?
>>
>> Mathematica says (ln 10077696) / (ln 36), which numerically evaluates
>> to 4.5, which then led me to try 36^(9 / 2), which indeed evaluates to
>> 10077696. In the much smaller example log_4 8, Mathematica unhesitantly
>> says
>> 3 / 2. I'm wondering if there is some subtlety I have missed, or if maybe
>> machine precision makes some kind of difference here.
>>
>> Al
>>
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